GENERAL EQUILIBRIUM

AND WELFARE ECONOMICS

INTRODUCTION

In this chapter we bring the producer and consumer side to­ gether into one model (see Figure 4.1). This will allow us to estab­ lish the third condition for Pareto optimality which explains optimality for the entire economy. The branch of economics con­ cerned with this whole economy perspective is called welfare eco­ nomics. Neoclassical welfare economics is based on three argu­ ments first set forth by Adam Smith in The Wealth of Nations pub­ lished in 1776. These are: (1) humans are motivated by self-interest, (2) if individu,als are allowed to pursue their own self-interests, competition wUI automatically lead to the best situation for society as a whole, and (3) it follows that the best economic policy a government can pursue is to allow the greatest possible freedom for individuals to pursue their own self-interest. The first two of these arguments are the basis for neoclassical theory, and the third argument is the basis of neoclassical economic policy. Throughout this chapter we continue to deal with a barter or a pure exchange economy. Prices will not be introduced until the

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next chapter. Among the assumptions made so far are (1) individu­ als and firms are fully informed of the characteristics of all goods and productive inputs traded, (2) the initial amounts and distribu­ tion of these goods and inputs are given, and (3) individuals are able to freely trade their given endowments of goods and inputs. Given these assumptions, free exchange between individual con­ sumers and between firms will lead to a Pareto optimal situation, where no one can be made better off without making someone else worse off, and where resources are allocated so that the production of one good cannot be increased without decreasing the production of another.

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If we randomly pick a point on the production possibilities frontier,

we pick a fixed amount of beef and Brazil nuts produced, and thus set the endowment of our society with these two goods. Going back to our assumptions in consumer theory, this means that for each point on the production possibilities frontier, we can construct a particular Edgeworth box diagram showing the particular initial combination of beef and Brazil nuts at that point. If consumers are allowed to trade freely, they will end up somewhere on the con­ tract curve showing all the possible Pareto optimal allocations of the specific amounts of these goods. This procedure is shown in Figure 4.2 which illustrates how we can bring together Pareto optimality in production and in consumption to establish the nec­ essary condition for Pareto optimality in general, that is, for the entire society of consumers and producers.

FIRMS

1_____.

Goods Good X

HOUSEHOLDS

Figure 4.1 The Producer/Consumer Relationship. GoodY

GENERAL EQUILIBRIUM IN EXCHANGE The third condition for Pareto optimality can be derived from the production possibilities frontier described in Chapter 3. We showed that all points on the production possibilities frontier rep­ resent different combinations of goods X (beef) and Y (Brazil nuts) that can be produced when society's resources (in our examples, capital and labor) are used in the most efficient manner possible. In other words, it shows all the possible combinations of goods that can be produced when Pareto optimality in production is achieved.

Figure 4.2 Pareto Optimality in General.

The slope of the production possibilities frontier shown in Figure 4.2 gives the rate of product transformation (RPT).

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willing to substitute beef for Brazil nuts and still maintain the same level of satisfaction (remain on the same indifference curve). THE RATE OF PRODUCT TRANSFORMATION SHOWS THE ,RATE AT WHICH THE AMOUNT OF ONE GOOD CAN BE REDUCED AND THE AMOUNT OF THE OTHER INCREASED WHILE REMAINING ON THE PRODUC­ TION POSSIBILITIES FRONTIER. IN OTHER WORDS, IT SHOWS THE RATE,AT WHICH ONE GOOD CAN BE GIVEN UP SO THAT MORE.oF ANOTHER GOOD CAN BE PRODUCED, CONSIDERING THE GIVEN ENDOW­ MENTS OF RESOURCES AND THE TECHNOLOGICAL CAPABILITIES OF A SOCIETY.

Recall that the slopes of the indifference curves within the Edgeworth box in Figure 4.2 show the marginal rate of substitution of beef for Brazil nuts, or the relative amount of satisfaction (that is, the ratio of marginal utilities) these two goods generate for our two consumers Alex and Bertha. For the consumer side, we can say that at any point on the contract curve, the marginal rate of substitution between the two goods is the same for both consumers. The third and final condition for Pareto optimality is: P~RETO CONDITION

MRSB YX

III: RPTyrooX = MRS\X=

PARETO OPTIMALITY FOR CONSUMERS AND PRO­ DUCERS ,IS ACHIEVED' WHEN THE RATE OF PRODUCT TRANSFORMATION BETWEEN GOOD

X AND GOOD

YIN PRODUCTION IS EQUAL TO THE MARGINAL RATE OF SUBSTITUTION BETWEEN THESE GOODS IN CON­ SUMPTION.

This condition states that resources and goods are optimally allocated when the rate at which beef (good X) must be given up (that is, not produced) in order to free up resources to produce enough Brazil nuts (good Y) to remain on the production possibili­ ties frontier, is exactly equal to the rate at which consumers are

The best way to see that condition III is Pareto optimal is to consider a situation in which it is not met. Assume that the rate of product transformation of beef into Brazil nuts is 1:2, that means if one pound less beef is produced, enough capital and labor is freed up so that producers are able to make two more pounds of Brazil nuts. Suppose the marginal rate of substitution is 1:1, that is, con­ sumers are willing to give up one pound of beef for one additional pound of Brazil nuts without reducing their overall level of utility, or satisfaction. In this situation optimality has not been reached. A change in production can be made which will increase the total utility of this society. If one pound less beef is produced, enough resources are freed to produce two additional pounds of Brazil nuts, since the RPT is 1:2. But because the consumers' MRS is 1:1, even one extra pound of Brazil nuts in exchange for the one pound of beef given up would keep their overall satisfaction level the same. The one extra pound of Brazil nuts, therefore, increases the consumers' utility level. Given the assumption that more is always better (non-satia­ tion), this simple two-good (two-firm), two-consumer society is undeniably better off after making these changes, and producing more Brazil nuts and less beef. Only when the rate of product transformation is equal to the marginal rate of substitution is a situation achieved in which no further change can improve the welfare (as measured by efficiency in allocation) of this society. Such a Pareto optimal position is shown in Figure 4.2, where the slope of the production possibilities frontier (the RPT) at point 1 is equal to the common slopes of the indifference curves (the MRS) at point 2 in the Edgeworth box for consumers A and B. When the third Pareto condition is met, we say the economy is in general equilibrium. The word general indicates that we are talking about the whole economy of producers and consumers. The word equilibrium means that once the third Pareto condition has been established the economy will be stable, unless disturbed by some outside influence, and if disturbed, it will always tend to return to its equilibrium state.

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This general Pareto optimal situation is the goal of neoclassical economics. Given some initial endowment of resources (produc­ tive inputs) that produce a certain amount of goods and services, and given some initial distribution of the resources among produc­ ers, and given an initial distribution of the goods produced among consumers, unhindered exchange will lead the economy to the most efficient allocation of goods and resources. We can take the notion of Pareto optimality one step further by constructing a utility possibilities frontier. A utility possibility fron­ tier is derived in the same manner as the production possibilities frontier we constructed from the contract curve in an Edgeworth box for production. It shows all the Pareto optimal combinations of utility of consumers A and B resulting from various initial distribu­ tions of goods X and Y. We can derive such a utility possibilities curve for all the Pareto optimal combinations of goods X and Y that result from the initial endowments of these goods given by all the points on the production possibilities frontier. Figure 4.3 shows several utility possibility frontiers that can be constructed using the information in a contract curve in consumption such as the one shown in Figure 2.6. We cannot use neoclassical notions of efficiency to say which point on a utility possibilities curve is "best." We can, however, use the information contained in all the utility possibility curves to construct one grand utility possibility frontier. THE GRAND lffillTY POSSIBllffiES FRONTIER SHOWS All THE PARETO OPTIMAL COMBINATIONS OF lffillTY CONSUMERS MAY DERIVE FROM THE CONSUMPTION OF All POSSIBLE COMBINATIONS.OF GOODS THAT ARE PRODUCED WHEN .INPUTS ARE USED IN THE MOST EFFICIENT MANNER POSSIBLE.

We can see in Figure 4.3 that if we move from a point such as 3 to point 1, we have increased the utility of Alex while keeping the utility of Bertha the same. Likewise, if we move from point 3 to point 2, we increase the utility of Bertha without hurting Alex. A move to any point between 1 and 2 on the grand utility possibilities frontier, U, makes both Alex and Bertha better off. The grand utility

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Utility of

Consumer

A (Alex)

Utility of Consumer B (Bertha)

Figure 4.3 The Grand Utility Possibilities Frontier.

possibilities curve is an "envelope" curve constructed by taking the outermost points of the collection of all the possible utility possibil­ ity frontiers. Any point interior to the grand utilities possibilities frontier will be less preferred according to the Pareto criterion.

THE SOCIAL WELFARE FUNCTION We saw in Chapters 2 and 3 that compared to points off the contract curve, any combination of goods or inputs on the contract curve is "optimal." But nothing in the theory allows us to pick the "best" point on the contract curve itself, or the "best" point on the grand production possibilities frontier. This means that using the Pareto criterion alone, we can not make any value judgements about the "fairness" of the distribution of goods between consum­ ers. Likewise, we cannot say anything about whether the resource allocation resulting from individual preferences is really desirable for society as a whole, or whether the level of total production is desirable. To address these questions of scale and distribution, we need to step outside the framework of neoclassical analysis. One analytical tool to address the question of the fairness of the distri­ bution of goods between consumers is to construct a social welfare function (W). It may also be called an iso-welfare function, since all the points on a given social welfare curve represent the same level

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Utility of

Consumer

A (Alex)

Ws W2 W, Utility of Consumer B (Bertha)

Figure 4.4 The Social Welfare Function.

of total social welfare. Figure 4.4 shows three welfare functions, W j , W z, and W 3, which represent something like collective "utility functions" for the entire society. The social welfare function embodies the welfare judgments of society as to the fairness, or desirability, of the distribution of goods among consumers. Higher utility (resulting from more con­ sumption) is assumed to be better than lower, so the goal is to pick the highest level of welfare possible given the constraint imposed by the grand utility possibilities frontier, that is, by the highest possible level of utility this society is capable of reaching given its production possibilities. In Figure 4.4 this is shown by point 1 (called a constrained bliss point), where the social welfare function W z is just tangent to the grand utility possibilities frontier. The economy would be better off at some point on the higher social welfare function, W 3, but this function is not attainable given this society's endowment of resources and its level of technology. The social welfare function allows us to pick the single point on the grand utility possibilities frontier that corresponds to a specific point on the contract curve for consumption that society deems "best." By implication, this also allows us to pick a corresponding

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point on the production possibilities frontier indicating the most socially desirable mix of goods X and Y. Referring to Figure 4.4, we can see that as we move from one point to another on the utility possibilities frontier, one person is made worse off (her utility is lowered) in order to make someone else better off. For example, by moving from point 2 to point 1, in Figure 4.4, consumer A (Alex) is made better off. But to achieve that higher utility for Alex, Bertha (consumer B) must give up utility and be made worse off. Such a move would not be allowed according to the Pareto criterion. A situation that reduces the utility of one of the consumers in ex­ change for another's utility increase requires a value judgement about the absolute levels of utility of these consumers that goes beyond the relative utility framework of Pareto optimality. There is nothing within the basic neoclassical model of pro­ ducer and consumer behavior that allows us to construct a social welfare function. The neoclassical concept of efficiency can only take us to the production possibilities frontier, or to the grand utility possibilities frontier. To pick out a single point on that frontier from among the infinite possibilities, we must leave the neoclassical framework and include additional considerations about the social desirability of the various possible utility combinations between members of society. The fact that a social welfare function has to be constructed based on an external set of rules, so that a socially optimal allocation of goods and inputs can be determined, is the Achilles heel of neoclassical theory. Once we are forced to come up with rules of choice to pick a particular Pareto optimal combination of goods and a particular distribution of these goods, we can no longer avoid addressing the ethical questions we have dodged so far. The necessity of a social welfare function was first discussed by the economist Abram Bergson in 1938. Since then a number of economists and social philosophers have suggested rules to con­ struct such a function. Nicholas Kaldor suggested the simple rule that a move from one point to another on the utility possibilities frontier is justified if the person gaining from the move values her gains more than the person who loses values his loss. In other words, if Alex's gain in utility is larger than Bertha's loss, then the redistribution of goods between the two is justified. Tibor Scitovsky

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amended the Kaldor criterion by adding the condition that after a change is made, we must be sure that society would not be better off by returning to the original situation. An interesting contribution to the social welfare debate was made by the philosopher John Rawls. Rawls begins with a thought experiment. Suppose that you are to be placed within a society without knowing ahead of time what your social standing would be, that is, what your income would be compared to everyone else? What sort of society would you pick in terms of its income distri­ bution? Would you pick a society with a very unequal income distribution where your chances of being poor are very high, with a small chance of being wealthy, or would you pick a society with a relatively egalitarian income distribution? Rawls argues that most people would pick the latter. He argues further that we should construct our social welfare function on the basis of providing as much income equality as possible, until we reach the point where a move to more equality would reduce the total output of society and reduce the income of the worst-off person. Rawls' argument assumes that people are risk averse and thus unwilling to take the chance of ending up poor, or that they are altruistic and care about another's fate, not just their own.

GENERAL EQUILIBRIUM THEORY AND THE BIOPHYSICAL WORLD While the welfare considerations that enter the general equilib­ rium conditions of Pareto Optimality force us to leave a strictly neoclassical world, the assumptions made in that world still enter the general equilibrium analysis unchanged. The relevant time frame is still the immediate present, consumer tastes and produc­ tion technologies are given, and place as location and social and ecological context is not considered. The analysis is assumed to be universally applicable, and the consequences of changing the start­ ing conditions, such as the initial distribution of goods or inputs, remain outside the framework of optimality. In other words, the broader consequences of individual actions are not considered in the general equilibrium framework. There are no feedbacks in this analytical framework and therefore no need for caution, no need for future orientation, and no need for prevention. The better-off/

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worse-off parameters of Pareto optimality are still determined by the quantity of goods available for consumption, resource effi­ ciency is still determined by currently known use alternatives, and the relevant time frame is still the immediate present disconnected from past or future. The discussion of what determines social welfare has been driven by the goal of material accumulation. More is better while qualitative differences are ignored. The limits to this notion of welfare are becoming increasingly evident. No one would deny that basic material needs must be met in order to achieve some minimal socially acceptable level of welfare. But food, clothing, shelter, or even cars and VCRs are not all that determines our well­ being as individuals or as a society. A recent survey conducted in Japan, the country celebrated for its miraculous achievements in economic efficiency and growth, speaks to the problem of adequate welfare measures. In a broad-based survey, the Japanese were asked to choose the two most important social changes from a list of ten. Of the 68 percent who responded, 53 percent thought Japan had transformed itself from a poor into a rich nation, and 46 percent said Japan was no longer thrifty. However, fewer than 3 percent of the respondents thought Japan had become a happier nation. Our well-being is affected by social structures and support systems like families, neighborhoods, and social context, by the well-being or suffering of others, by the quality of our natural environment affecting our ability to use rivers for swimming, parks for walking, and streets or backyards safely for children's play, and by the material things available to us. The costs of social and environmental change may be qualitative, as in lost comfort levels or increased stress, but they may also be quantifiable, as in in­ creased health care or security needs. What does all this mean for our simple example of Brazil nuts and beef (two goods), and capital and labor (two inputs)? If more people can be fed by producing Brazil nuts than beef, the two cannot be simply equated as generating comparable utility levels since the social welfare effects of the consumptions of these two goods are very different. Likewise, if the same number of calories can be produced from Brazil nuts instead of beef with less land

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being used or destroyed, smaller losses in biological diversity and less soil erosion and fertility loss, then the use of inputs for beef production results in less welfare, particularly for future genera­ tions. If traditional practices of producing beef or Brazil nuts pre­ serve soil and water quality and strengthen social support systems, then the lower yields resulting from such traditional practices may be socially advantageous rather than negative. If an increase in beef production benefits those whose calorie intake is already above 3,500 calories per day, while an increase in the production of Brazil nuts benefits those whose daily calorie intake is much lower, the social evaluation of beef versus Brazil nuts is complicated by the question of who benefits and who loses. All these examples show the limits of a social welfare function derived from individual tastes as the basis for welfare maximiza­ tion. They also point to the complex questions involved in interper­ sonal comparisons of welfare. Can one person's benefits outweigh another person's loss? Despite the fact that neoclassical economists would generally argue that it is impossible to compare interper­ sonal utility levels, it is recognized that the definition of a social welfare function is necessary as a starting point for general equilib­ rium analysis. Social Welfare and Ethics

Humans are social beings. What happens to others affects us. Humans act as social agents embedded in a social context. This has led to a somewhat redefined version of the neoclassical notion of social welfare based on strictly individual preferences. Altruism, for example, is considered one kind of individual preference, as are sadism or masochism. One might also argue, for example, that social inequality, which leads to unrest or a level of air pollution that impacts ones quality of life, would be avoided by a rational­ acting, individual interest maximizer. Some have applied Rawls' understanding of utilitarian ethics to the question of intergenerational environmental equity. If we did not know which generation we would be placed in, how would this affect our attitude toward resources use or pollution? The assumption is that if we thought we might be placed in a society that exists 100 years from now, we would be more likely to be

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concerned with protecting the biosphere and preserving natural resources. Others, however, suggest that individual preferences are not enough to address the dilemmas and tensions between individual decisions and their impact on social and ecological con­ texts. Time, however, does seem to influence our perception of indi­ vidual versus social interests. A short-term view seems to under­ mine more altruistic or ecologically conscious behavior. Game theory experiments testing strategic individual behavior confirm the im­ portance of time frame. Experimental results have shown that under conditions of long-term durable relationships, cooperative strategies were far more successful than competitive ones. Tran­ sient, short-term relationships, on the other hand, seem to under­ mine the benefits of reciprocal and mutual solutions. Cultural differences, too, determine the ways in which indi­ vidual versus social and ecological benefits are perceived and evalu­ ated. In many societies, Adam Smith's understanding-that the individual pursuit of self-interest also leads to the best interest of society as a whole-would be turned around. The individual's well-being is intricately connected to the well-being of the commu­ nity, and thus the welfare of the whole is decisive. Examples of a mutual and reciprocal understanding of the individual as part of a larger social and ecological context are found in the belief systems of indigenous peoples. What happens to nature is inseparably connected to the fate of humans. The neoclassical framework as­ serts not only a particular kind of economic understanding but also a particular cultural perspective of the relationship between indi­ viduals and their social and ecological context. In many ways the global environmental problems we face have added new fuel to the welfare discussion. They have added a new dimension to the interconnectedness between individual and so­ cial context. The medium by which we are connected in a very real way over time and over space is the global ecosystem we share. The African woman who has to walk further to get water and work longer hours on drought-affected soils suffers from the conse­ quences of climate changing emissions that stem from U.S. or European factories, heating systems, and automobiles. But the North is also affected by the low-tech inefficient and high-emission, coal­

70 • ECONOMIC THEORY FOR ENVIRONMENTALISTS burning plants that generate electricity in many parts of the world where low emission technology is unaffordable. However, adding ecological considerations does not solve the problem of ethical dilemmas raised by the question of social welfare. It merely en­ larges the dimensions of the dilemma. All may be affected by such global problems as climate change, ozone depletion, or biodiversity loss. But rather than equalizing them, environmental consequences are likely to exacerbate social inequalities. Examples of toxic waste sites located in minority neighborhoods, waste shipments to so­ called third world countries, or the inability to cope with mounting health effects have made it clear that the poor are also more likely to suffer from the consequences of environmental degradation and unsustainable management practices. The question of what defines a socially optimal level of production and consumption is not solved as we confront their effects on the biophysical world, but it may well be brought into sharper focus. Beyond Human Welfare

Another question the social welfare framework avoids is how we consider the welfare of the non-human, biophysical parts of our world. Do they deserve their own consideration, or do we evaluate them simply based on their usefulness to humans and their impact on human well-being? In the 1930s Aldo Leopold called for a "land ethic" that would respect the rights of nature. This point of view has continued to grow into today's environmental movement with organizations whose members number in the millions. Calls for the ethical treatment of nature are becoming more and more accepted as a result of the growing scientific evidence blurring the distinc­ tion between humans and the rest of the animal kingdom. The ecological ethic of ecofeminism is an ethic of eco-justice, which focuses on the links between social domination and the domination of nature. It sees the roots of the dual oppression of exploited humans and exploited nature in the separation of nature and culture established by the scientific revolution, patriarchal religion, and the dominant psychology of a rights-based rather than a responsibility-based ethic. For the social welfare of humans to be fully considered, the welfare of nature and the links between nature and humans have to be reevaluated.

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SUMMARY The final step in constructing the general equilibrium of neo­ classical theory integrates production and consumption into a single framework. In doing so we keep all the assumptions we have made so far-more is better, present tastes and priorities, current knowl­ edge, and technological sophistication determine the better-off or worse-off of neoclassical optimality. In order to address the ques­ tion of how to determine the most socially desirable Pareto optimal point of production and consumption, our analysis threw us head­ long into a discussion of the social welfare function. The social welfare function has an uneasy place in neoclassical theory. Although it is recognized that such a function is theoreti­ cally necessary as a starting point for general equilibrium analysis, neoclassical economists generally argue that interpersonal com­ parisons of utility cannot be made. In the neoclassical world, the sanctity of selfish, individual decisions dictates that a social wel­ fare function should be based on individual preferences (although "altruism" is recognized as one kind of individual preference). In reality, however, all societies implicitly construct a social welfare function when they make political decisions affecting income dis­ tribution and the use of natural resources. Various kinds of transfer payments to the poor, the graduated income tax, environmental regulations, and zoning laws, all embody some notion of a social welfare function. In all these cases, society is taking something from one group and giving it to another, for the good of society as a whole. Apart from the ethical questions involved in determining a society's welfare function, there are serious measurement prob­ lems as well.,How can we measure a society's welfare and what criteria do we apply? This question can not be answered by eco­ nomics alone but requires that deep moral and ethical questions be addressed. The necessity of a social welfare function opens the door to all sorts of environmental policy questions. Is there a "common good" in protecting certain environmental features that should override individual preferences? Should the social welfare function be broad­ ened to include future generations? Should the social welfare func­ tion take into account the well-being of other species? Despite its claim to value neutrality, the social welfare function makes explicit

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that the analytical framework of neoclassical theory has a particu­ lar ethical basis; the ethics of a self-interest-oriented individual at a given point in time. The establishment of the conditions for general equilibrium in a pure exchange (barter) economy completes the first part of the neoclassical analysis of the economy. The next part, covered in Chapter 5, establishes the conditions under which a perfectly com­ petitive economy will ensure that Pareto optimality is met, that is, when a perfectly operating price system will exactly duplicate the result achieved in the barter economy described in this chapter.

SUGGESTIONS FOR FURTHER READING Booth, Douglas. Valuing Nature: The Decline and Preservation of Old­ Growth Forests. Rowman & Littlefield, Lanham, Maryland, 1994. Bormann, Herbert and Stephen Kellert. Ecology, Economics, Ethics: The Broken Circle. Yale Univ. Press, New Haven, Connecticut, 1991. Hirsch, Fred. Social Limits to Growth. Harvard Univ. Press, Cam­ bridge, Massachusetts, 1976. Leopold, AIda. A Sand County Almanac. Oxford Univ. Press, New York,1966. Ostrom, Elinor. Governing the Commons: The Evolution of Institutions for Collective Action. Cambridge Univ. Press, New York, 1990. Quirk, James and R. Saposnik. Introduction to General Equilibrium Theory and Welfare Economics. McGraw-Hill, New York, 1968. Rawls, John. A Theory of Justice. Harvard Univ. Press, Cambridge, Massachusetts, 1971. Sagoff, Mark. The Economy of the Earth. Cambridge Univ. Press, New York, 1988. Schor, Juliet. The Overworked American. Basic Books, New York, 1991. Scitovsky, Tibor. The Joyless Economy. Oxford Univ. Press, New York, 1976.

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Sen, Amartya and Bernard Williams, (eds.). Utalitarianism and Be­ yond. Cambridge Univ. Press, New York, 1982. Shiva, Vandana. Staying Alive. Women, Ecology, and Development. Zed Books, London, 1989. Society and Nature, Special Issue on "Feminism and Ecology," 2 (1),

1993. See also the many articles on economics and ethics in the jour­ nals Ecological Economics, Environmental Ethics, Environmental Val­ ues, The International Journal of Social Economics, and The Review of Social Economy.